study of fluctuations on isospin symmetry in au+au collisions at rhic-phenix

2002/3/25 Tomoaki Nakamura Hiroshima Univ. 1

Study of Fluctuations on Isospin Symmetry

in Au+Au Collisions at RHIC-PHENIX

Tomoaki Nakamura / Kensuke HommaHiroshima Univ.

for the PHENIX Collaboration


1. Physics Motivation 2. PHENIX Experiment3. Multi Resolution Analysis (MRA)4. Result5. Summary

Contents


Centauro Type Event

(High Energy Cosmic Ray Experiment)• (Brazil-Japan collaboration in Bolivia)

Y.Fujimoto and S.Hasegawa, Phys. Rep. 65, 151 (1980)

• (JACEE) J.J.Lord and Iwai, Paper No. 515, International Conference on High Energy Physics, Dallas (1992)

(High Energy Accerarator Experiment)• (UA5) K. Alpgard rt al., Phys. Lett. 115B, 71

(1982)• (CDF) P.L.Melese for the CDF Collaboration

XIth Topical Workshop on ppbar Collider Physics (1996)

• (MINIMAX) T.C.Brooks et al., Phys. Rev. D 55, 5667 (1997)

(High Energy Heavy Ion Experiment)• (WA98) Tapan K. Nayak et al.,

Nucl.Phys.A663:745-748, (2000)

O : Photon, + : Charged Particle

Anti Centauro


Disoriented Chiral Condensate

NN

NN

NN

NNAI

)()(

4

)(2)()(

0

0

3

(Quench Mechanism) K.Rajagopal and F.Wilczek : Nucl. Phys. B379, 395 (1993)

Fluctuation of Asymmetry as a function of pseudo rapidity

du

edu i 5

HvL ii

222

41

21

Chiral Transformation

Linear sigma model

Quench

σ

π

V

σ

π

VRestoration

QCD vacuumDCC


PHENIX Experiment atGeVsNN 130

Z

Associated PC3 Cluster

PC1 Cluster

Rejected EMCal Cluster

BBC Z-Vertex

•Pad Chamber 1 (PC1)

•Pad Chamber 2 (PC2)

•Lead Grass Electro-Magnetic Calorimeter (EMC)

o5.220

35.035.0

Using Magnetic Field-off data

Gamma like Cluster (EMC)

Charged Track (PC1, PC3)


Correlation between Charged Tracks and Gamma like Clusters

(MC with Full Reconstruction)(Real Data)


Isospin Asymmetry

clusterliketrackPC

clusterliketrackPCI NN

NN

NN

NNA

)()()()()(

3

δAI3

Domain Size

Deviation Size

Domain Position

pseudo rapidity


Multi Resolution Analysis (MRA)

Wavelet function

Scaling function

Level j-1 : 2j-1 bins Level j : 2j bins

φ(2x) = 1/√2 {φ(x) + ψ(x) }φ(2x-1) = 1/√2 {φ(x) - ψ(x) }

-0.7

＝( － )

( ＋ )

0.7φ(x)

0.7ψ(x)

x

x

-1

1

1

φ(2x-1)

x-1

1

1

φ(2x)

x

-0.7


Signal Decomposition j : resolution levelk : k-th bin in pseudo rapidity Cjk : coefficients of φDjk : coefficients of ψ

Signal

φ ψ

k k+

+

+

+

22 20j=4

j=3

j=2

j=1

j=0

Cjk

Djk

j → Domain Size

k → Phase Space Position

Djk → Deviation Size


Djk Max distribution

-0.6 -0.4 -0.2 0.0 0.2 0.4 0.6[Djk max]

j=5Δη=0.0219

j=4Δη=0.0438

j=3Δη=0.0875

j=2Δη=0.1750

j=1Δη=0.3500

•Red : Real Data PHENIX B-field off data √sNN =130GeV Selected 44,180 events from minimum bias 700k events.

•Blue : MC with Full reconstruction HIJING √sNN =130GeV Selected 25,281 events from minimum bias 200k events


Probability of Large Djk Max Event

[Djk max]

Djk Max (J=5) (Nch = 10, Nγ=10)

99.999% exclude

99.95% exclude

99.98% exclude

DjkMAX

NNkkA

kBkB

ch

j

jjch

'

)(

'))(),((

Binomial Distribution

jj

kNjkjkN

jN

P

PPCkB ch

chch

2

)1()()(


Event Sample (1)

Asymmetry (-) Asymmetry (+)PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

j=5　 Δη=0.0219


Event Sample (2)

PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

j=4　 Δη=0.0438 j=3　 Δη=0.0875


Event Sample (3)

PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

j=2　 Δη=0.1750 j=1　 Δη=0.3500


Total Energy (Centrality)

Total Energy of Electro-Magnetic Calorimeter

j=5 Δη=0.0219

j=4 Δη=0.0438

j=3 Δη=0.0875

j=2 Δη=0.1750

j=1 Δη=0.3500

[GeV]


Summary• The total 155 anomalous events are found by MRA. Th

e definition of “anomalous events” is the events above thresholds which exclude 99.999% of normal events, if those normal events are based on combination of the binominal distributions.

• We are investigating the nature of the events with large deviation from binomial, whether those are coming from PHYSICS or detector.

Level j=5Δη=0.0219

j=4Δη=0.0438

j=3Δη=0.0875

j=2Δη=0.1750

j=1Δη=0.3500

Number of Events 129 18 5 2 1

(# of anomalous events) / (selected total # of events) : 153 / 44,180


Backup Slide


Backup (1)

PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

PC1

PC3

EMC

Z [cm]

Z [cm]

Z [cm]

Phi [

rad]

Phi [

rad]

Phi [

rad]

j=1　 Δη=0.3500 Raw Cluster


Rejection of Asymmetric dense Cluster

TrackA TrackB

PC1 association cut --------- 3 cm

PC3 association cut 6 cm ---------

EMC rejection cut 6 cm 6cm

Z

associated PC3 cluster

PC1 cluster

Z

PC3 cluster

associated PC1 cluster

Rejected EMC cluster

BBC-Zvertex


Window shift method

Shift the start bin at eachresolution level.

Find djk max among all of levels.

This can determine the level(domain size) with the largestdeviation size. should appear here !

A symmetric structureappears in wrong level

djk is lower


Performance of window shift method

Success probability that a correct domain size is found

j=1 j=2 j=3 j=4 j=5 j=6 j=7

Deviation size Ns

Domain sizeof 28 / 2j

study of fluctuations on isospin symmetry in au+au collisions at rhic-phenix

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